A ball bounces on the inclinedplane such that it rebounds pe

A ball bounces on the inclinedplane such that it rebounds perpendicular to the incline witha

velocity vA. Determinethe distance R to where itstrikes the plane at B.

Given:

=30 deg

vA= 40  ft/s

Solution

= 30^o, vA= 40  ft/s, g=32.2ft/s²

choose along the incline down as +x, perpendicularto the incline up as +y

initial velocity v_x = 0, v_y =40 ft/s

acceleration a_x = gsin,a_y = -gcos

from A to B, displacement x = R, y = 0

y = v_yt + a_yt²/2 =0

so t = -2v_y/a_y =2v_y /(gcos)

R = v_xt + a_xt²/2 =gsint²/2 = gsin[2v_y/(gcos)]²/2 =2v_y²sin/(gcos²) =66.3 ft